Unit Circle Trigonometric Functions

The video tutorial explains the unit circle, a circle with a radius of one, and its significance in trigonometry. It describes how a triangle can be drawn within the unit circle, with the hypotenuse equal to the radius. The video then explores the angle theta and its corresponding coordinates, using 30 degrees as an example. It defines sine and cosine functions in the context of the unit circle and introduces other trigonometric functions such as tangent, cosecant, secant, and cotangent.

What is the radius of a unit circle?

• 2

• 3

• 1

• 0.5

In a unit circle, what is the hypotenuse of a triangle drawn within it?

• 0.5

• 3

• 1

• 2

For a 30-degree angle on the unit circle, what is the x-coordinate?

• 1

• 0.5

• √3/2

• 2

For a 30-degree angle on the unit circle, what is the y-coordinate?

• 1

• √3/2

• 0.5

• 2

In the unit circle, what does sine of an angle represent?

• radius

• x-coordinate

• angle

• y-coordinate

In the unit circle, what does cosine of an angle represent?

• x-coordinate

• y-coordinate

• radius

• angle

What is the formula for tangent in terms of sine and cosine?

• sine / cosine

• sine - cosine

• cosine / sine

• sine + cosine

What is the formula for cosecant in terms of y?

• y

• 1/y

• 1/x

• x

What is the formula for cotangent in terms of x and y?

• x+y

• y/x

• x-y

• x/y